#
Monadic approach to Galois descent and cohomology

##
Francis Borceux, Stefaan Caenepeel and George Janelidze

We describe a simplified categorical approach to Galois descent theory.
It is well known that Galois descent is a special case of Grothendieck
descent, and that under mild additional conditions the category of
Grothendieck descent data coincides with the Eilenberg-Moore category of
algebras over a suitable monad. This also suggests using monads directly,
and our monadic approach to Galois descent makes no reference to
Grothendieck descent theory at all. In order to make Galois descent
constructions perfectly clear, we also describe their connections with
some other related constructions of categorical algebra, and make various
explicit calculations, especially with 1-cocycles and 1-dimensional
non-abelian cohomology, usually omitted in the literature.

Keywords:
Descent theory, Galois theory, monadic functor, group cohomology

2000 MSC:
18C15, 18D10

*Theory and Applications of Categories,*
Vol. 23, 2010,
No. 5, pp 92-112.

http://www.tac.mta.ca/tac/volumes/23/5/23-05.dvi

http://www.tac.mta.ca/tac/volumes/23/5/23-05.ps

http://www.tac.mta.ca/tac/volumes/23/5/23-05.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/23/5/23-05.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/23/5/23-05.ps

TAC Home